In the end, Boston College was crossing its fingers hoping for a program-validating victory, and Duke was grabbing the game with both hands, refusing to let go.

The difference in this game wasn’t records or coaching résumés or McDonald’s All-Americans or Final Four banners. It was the gap between believing you can win and knowing you’re going to, the institutional knowledge of victory that a program such as Duke stamps every player with like a notary public.

Duke won because it’s Duke, and it expects to win. There is no stat in the box score for belief.

The college basketball blue blood of the fourth-ranked Blue Devils allowed them to pull out a 62-61 victory over BC on Sunday at Conte Forum. That blood was blue not just because of Duke’s elite status in the game, but the ice-water calm it exhibited trailing by 5 points with 2:15 to go after Eagles freshman guard Olivier Hanlan sank two free throws.

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Those would be BC’s last points. Duke escaped by scoring the final 6 points — a clutch corner 3-pointer by Quinn Cook and three free throws from Mason Plumlee, the last of which with 24 seconds to go set up a frantic finish.

“We didn’t lose the game. Duke won the game. They made plays down the stretch,” said BC coach Steven Donahue. “We didn’t play bad down the stretch, but they made more plays than us.”

Cook, who had been 2 for 10, drilled a 3 from the right corner with 1:58 left to pull the Dukies within 2 at 61-59. Plumlee, who had to work for every one of his 19 points and 10 rebounds, tied the game with a pair of free throws.

Plumlee was at the line again after he hauled down a defensive rebound on a good look from BC’s Joe Rahon and was fouled by Ryan Anderson. He made one of two free throws to give Duke the lead.

That set the stage for potential heroics and floor-storming hysteria at the Heights. But Hanlan missed a jumper in the lane and Anderson lost the ball in the ensuing rugby scrum after Cook knocked out his legs like he was a bowling pin.

Duke gets those calls or non-calls. BC gets a loss.

It was a sublime Sunday of college basketball in Chestnut Hill. This was way more fun than digging out your car like you’re part of an archaeology expedition or the Sisyphean feat of shoveling the driveway. It was heart-pounding hoops with a heart-breaking ending.

As Duke doyen Mike Krzyzewski, who picked up career win No. 948, said there are no great teams in college basketball this year, only good ones, including his own.

Plumlee and fellow senior Seth Curry, a dead-eye shooter who had 18 points, are nice players who will play in the NBA. But they make barely a ripple in the sea of tradition that is Duke hoops.

“There aren’t the powerhouses that there have been,” said Krzyzewski. “We’re going to see a lot of good basketball for the rest of this month, and you saw good basketball tonight.”

Without a marquee team or a marquee player this college basketball season has become score-watching whiplash, as top teams drop games.

Duke has been No. 1 two times this season and lost. Sunday’s survival could put them there for a third time with last week’s tumult in the top five, which saw everyone except for Duke go down.

That’s why Coach K wasn’t vituperating his team afterward. He knows that in a season like this style points are a luxury.

“I like that my team won and the way we had to win because nothing about tonight was easy. These are games anybody can lose and throughout the country everybody is losing them,” said Krzyzewski. “Our guys found a way to win against a team that was also deserving to win, so that’s a real good thing.”

Coach K’s kids looked a little lethargic in the first half. The Dukies didn’t arrive into the snow globe that is the Boston area until around noon on Sunday for a 6 p.m. game, their travel delayed by the winter storm.

Curry said he felt like he never really got his legs under him.

He wasn’t alone. BC played defense that would have made NFL defensive rookie of the year and former BC linebacker Luke Kuechly, who was in attendance, proud.

A Duke team coming off a season-high 98-point performance in a win over North Carolina State was limited to 40.4 percent shooting for the game and just 37 percent in the second half.

Duke trailed the entire first half until Plumlee, who had been 1 of 5, came alive and came down with an offensive rebound — the bane of BC’s evening. He went back up and scored while being fouled. The traditional 3-point play with a minute left put Duke up, 25-24.

The game was tied, 27-27, at the half after Plumlee got another offensive rebound and slammed it home with four seconds left.

Duke led most of the second half, but couldn’t put the Eagles in the rearview mirror.

Boston College took its first lead since 30 seconds into the second half when Anderson followed a Rahon missed lay-in with a basket that put the Eagles up, 57-55, with 4:55 to go.

BC led until Plumlee’s game-tying free throws with 46.6 seconds left.

If college basketball were purely a meritocracy BC would have won Sunday.

But bloodlines count, and sometimes so does the name on the front of the jersey.